1729 (number)

Peculiarities of the number 1729

Hardy - Ramanujan number

The number 1729 is also known as the Hardy - Ramanujan number. It is the smallest natural number for which there are exactly two representations as a sum of two cubes.

Numbers with this property are called Taxicab numbers. The names of Hardy - Ramanujan number and Taxicab number refer to an anecdote, after the mathematician S. Ramanujan is said to have made ​​his mentor Godfrey H. Hardy pointed out that the number of the taxi used by this was a special number.

Sphenische number

Is the product of exactly three different prime numbers and thus a sphenische number. The factors are the three smallest primes cheerful.

Carmichael number

1729 is a Carmichael number, because for all bases (= 7 · 13 · 19 1729 ) have in common no prime factor 1729, the following applies:

It is the smallest constructed according to the method of Chernick Carmichael number, ie the smallest Carmichael number of the form

Harshad number

The 1729 is also Harshad number, that is, it is divisible by the sum of their digits: